From: ISMB-93 Proceedings. Copyright © 1993, AAAI (www.aaai.org). All rights reserved.
A Constraint
Reasoning
System for Automating
Sequence-Specific
Resonance Assignments
from
Multidimensional
Protein
NMR Spectra*
Diane
E.
tDepartment
Zimmermant~
of Computer
and
Casimir
A.
Kulikowskit
and
Gaetano
T.
Montelione~
Science
and J~Center for Advanced Biotecknology
and Medicine
Rutgers University
Piscataway
NJ 08854
Abstract
resonate in the presence of a magnetic field. Twodimensional NMI~is based on the analysis of crossAUTOASSIGN
is a prototype expert system depea~s which reflect the resonance frequencies of two
signed to aid in the determination of protein
nuclei interacting with one another. Similarly, threestructure from nuclear magnetic resonance (NMR)
dimensional NMRexperiments yield crosspeaks remeasurements. In this paper we focus on one of
flecting the frequencies of three interacting nuclei.
the key steps of this process, the assignment of the
Crosspeaks axe detected between atoms that interobserved NMRsignals to specific atomic nuclei in
act either "through-bonds" (when nuclei axe separated
the protein; i.e. the determination of sequenceby 3 or fewer chemical bonds) or "through-space"
specific resonance assignments. Recently devel(when intexatomic distances axe less than about
oped triple-resonance (XH, 15N, and 13C) NMRexA). These interactions axe selectively detected by difperiments [Montelione e$ al., 1992] have provided
ferent types of NMRexperiments [Wuethrich, 1986].
an important breakthrough in this field, as the
The newly developed NMRexperimental techniques
resulting data axe more amenable to automated
(Logan e~ M, 1992; Montelione c~ al, 1992; Lyons
analysis than data sets generated using convenand Montelione, 1993a; Lyons ef al, 1993b) which
tional strategies [Wuethrich, 1986]. The "assignprovide the three-dimensional data analyzed by AUment problem" can be stated as a constraint satTOASSIGNinvolve interactions
between backbone
isfaction problem (CSP) with some added com15N atoms and groups of residue-specific
protons in
plexities. There is very little internal structure
isotope-er~iched protein samples. These are called
to the problem, making it difficult to apply subCA-TOCSY[Lyons and Montelione, 1993a] and COgoaling and problem decomposition. Moreover,
TOCSY[Montelione e~ al., 1992] experiments.
the data used to generate the constraints are inThe process of protein structure determination by
complete, non-unique, and noisy, and constraints
NMRinvolves four principal steps [Wuethrich, 1986].
emerge dynamically as analysis progresses. The
traditional inference engine is replaced by a set
In the first step, networks of protons which interact
of very tightly-coupled modules which enforce exwith one another through chemical bonds are identitensive constraint propagation, with state inforfied. Each such network is called a proton spin system,
mation distributed over the objects whose relaand corresponds to a separate - but as yet unidentiffed - amino acid in the protein. Next, sequencetionships axe being constrained.
AUTOASSIGN
specific assignments for these spin systems are deprovides correct and nearly complete resonance assignments with both simulated and real 3D tripletermined by establishing their respective positions in
resonance data for a 72 amino acid protein.
the polypeptide sequence. In the third step, conformational constraints axe generated by correlating the
fhrougl~-space interactions detected in nuclear OverBackground
hauser effect (NOE) experiments with the resonance
frequencies identified in the previous two steps. FiThe basic nuclear magnetic resonance experiment
nally, structure generation programs axe used to comyields a one-dimensional spectrum of peaks reflectpute three-dimensional models of the protein satising the different frequencies at which various nuclei
fying these conformational constraints.
AI systems
have
been
developed
which
perform
this
last step
*Support for this work was provided in part by grants
[Lichtaxge e~ al., 1987]; [Edwards e~ al., 1992]. AUfrom The National Institutes of Health (GM-47014)and
TOASSIGN
is an object-oriented
expert system which
The National Science Foundation (DIi~-9019313). D.Z. was
uses constraint reasoning to solve the second step, i.e.
supported by a Biotechnology T~aining Grant from The
National Institute~ of Health (GM-08339)
the sequential assignment problem.
Zimmerman
447
Aminoacid
Listofident~ied
sloin
systems sequence
.~
_ ,~
variablesand
d domains
CO-T~
sloe
c’Ixa
,b
pruningof |
searchspaceJ
Preliminary
assi~ents
andlinks
F"
In
es
1 consistenci
~itesative
h
Sequencesloecific
assigm~ents
Figure
1: Overview of AUTOASSIGN
Overview
of AUTOASSIGN
The problem which AUTOASSIGN
solves can be defined as follows:
Given: A (complete) list of spin systems,
the anfino acid sequence of the protein, and
the inter-residue sequential connectivity information implied by a list of observed CO-TOCSY
[Montelione et al., 1992] crosspeaks;
Find: A one-to-one mapping of spin systems to
sequence-specific amino acids which is most consistent with the spin system connectivity information implied by the CO-TOCSYspectra.
Or
equivalently, impose a complete order on the list
of spin systems by establishing a complete set of
adjacency relations among them.
Figure 1 gives a high-level overview of our approach.
The expertise involved in performing this task interleaves simple geometric pattern matching with logical consistency reasoning using domain-specific knowledge. Each spin system specification submitted to AUTOASSIGNincludes the spin system type (see next
section), the nitrogen and amide proton resonance frequencies, and a list of aliphatic proton frequencies for
that residue. A spin system can be represented as a
set of points Migned parallel to the y axis in threedimensional space. The coordinates in the z and x
dimensions are defined by the magnetic resonance frequencies of the residue’s backbone nitrogen and amide
proton respectively. The aliphatic side-chain proton
frequencies of a particular spin system appear as a
"ladder" of crosspeaks occurring parallel to the y-axis
at the same point in the xz-plane.
448
ISMB-93
c,7"1
(a)
(b)
Figure 2: The CA- and CO-ladders of an Ala residue.
(a) The intra-residue CA-ladder reflects the interactions of Ala’s side-chain protons with its own backbone 15N and tt g nuclei. (b) The inter-residue COladder reflects the interactions of Ala’s side-chain proN
tons with the next residue’s backbone 15N and H
nuclei.
Each crosspeak within a spin system reflects an
intra-residue transfer of magnetization occurring between the three atoms which define its coordinates.
These crosspeaks can be detected by CA-TOCSY
experiments, and the resulting spin systems can be
referred to [Lyons and Montelione, 1993a] as "CAladders". The connectivity information contained in
the CO-TOCSY
spectra reflects inter-residue interactions effected by a redirection of the transfer of magnetization. Specifically, the magnetization of residue i~s
side-chain protons is transferred to the backboneamide
group atoms of residue i + 1. The relation between
"CA-ladders" and "CO-ladders ~ then, is analogous to
a rigid translation of each CA-lexlder to a new point
in the xz-plane corresponding to the adjacent residue’s
backbone anaide frequencies. This relationship is depicted schematically in Figure 2 and geometrically in
Figure 3.
Complete analysis of the CO-TOCSY
data involves
two subtasks. Since the CO-TOCSY
crosspeaks are
presented as a simple list of three-dimensional coordinates, the first task is to cluster these into CO-ladders.
Once this has been accomplished, CA-ladders can be
matched to CO-ladders to infer adjacency relations between spin systems. But in order to describe how sequence and connectivity information can be combincd
to arrive at sequence-specific assignments, we first need
to give a more detailed explanation of spin systems.
Amino Acid Spin Systems
Certain amino acids have spin systems which
axe uniquely characteristic
of that residue type
[Wuethrich, 1986]. Most residues bee, ring methyl
groups fall into this category, i.e., Ala, Thr, Val, Ile,
and Leu. Gly spin systems can also be uniquely identified as such, since they are the only residues bearing
two a-protons (Ha) and no side-chain. The remaining 14 residue types do not have unique spin system
patterns. Eight amino acids have what is called an
Y
Y
X
(a)
i+2
z
X
z
i+2
Figure 3: The CA- and CO-ladders of a sequence of 3 spin systems. (a) Each CA-ladder occurs in the xz-plane
a point defined by the spin system’s own amide group. (b) The CO-ladders occur at points in the xz-plane defined
by the sequence-adjacent amide group. The occurrence of only two CO-ladders reflects the fact that an N-terminal
spin system has no CO-ladder associated with its mnide group, while a C-terminal spin system has no "following"
CO-ladder on which to project its side-chain resonance values
_
H-~-H
O
O-H
H
Ala
(ALA)
Phe
(AMX)
Asp
(~X)
Figure 4: An ALAspin system followed by two AMXs.
AMX
spin system, which is characterized by a single
Ha and two H~ resonances. The AMX-type residues
include Set, Cys, Asn, Asp, Tyr, Phe, His, and Trp.
A second type of "non-specific" spin system is called a
LNG,and is characterized by having a single IT~, two
H#s, two H~s, and possibly additional hydrogen resonances. LNGspin systems include Arg, Lys, Met, Pro,
Glu, and Gln. Figure 4 illustrates the three spin systems associated with the tripeptide Ala-Phe-Asp, with
each proton network schematized by enclosing boxes.
Only those protons which are connected to other protons in the network by less than 4 bonds are included
in the boxes. Neither the aromatic protons of Phe nor
the hydroxyl proton of Asp are included in the spin
systems associated with those residues.
In AUTOASSIGN,whenever adjacencies
between
spin systems can be established,
the system checks
the sequence to see if a unique position is defined by
that segment of linked spin system types. One measure of the complexity of the problem is the "spin system degeneracy" (i.e. non-uniqueness) of the sequence.
For example, in a hexamer composed of Gly-AI~-ValThr-Ile-Leu, each amino acid generates a unique spin
system type which has only one possible position. In
contrast, a hexamer composed of six LNG-type amino
acids would be maximally degenerate.
The sequential assignment problem resembles in
many ways the classical problem in logic knownas the
"Five Houses Puzzle" [Van Hentenryck, 1989]. In that
problem, five individuals living on the same block each
have different professions, nationalities, pets, hobbies,
and so forth. Weare given only partial information,
such as "the Italian drinks tea" and "the Englishman
lives in a red house", and from these clues, must deduce who drinks water and owns a zebra. In our case,
the "individuals" are spin systems, and the order in
which different-colored houses appear is specified by
the amino acid sequence. The "clues" we are given
are the spin system adjacencies which can be inferred
by matching CA-ladders to CO-ladders. These clues
however, may be unreliable and incomplete.
The spin systems themselves may have extensive
overlap of their nitrogen and amide proton resonances
and/or non-distinctive patterns of side-chain resonances. Further complications arise from noise and
digitization errors in the spectra and incompleteness
in the observed set of crosspeaks. In most cases, each
pair of xz-values is uniquely defined by that residue’s
backbone resonance frequencies, but not always. When
both the x and z values overlap, the "rungs" of the associated ladders becomeinterleaved, and it is difficult
to determine which aliphatic protons are interacting
with which pair of backbone nuclei.
In summary, the sequential assignment problem is
similar to many constraint satisfaction problems but
with some additional challenges. In particular, many
of the constraints which must be applied to arrive at
a solution are not known a pr/or/, but must instead
Zimmerman449
be extracted as analysis progresses. The following section describes in more detail how we define sequential
assignment as an instance of constraint satisfaction.
Sequential
Assignment
as a Constraint
Satisfaction
Problem
(CSP)
In the CSPparadigm [Kumar, 1992], one is given a set
of variables, a set of values each variable can assume
(domains), and a list of constraints which further restrict howthese variables can be assigned. The goal is
to find a complete assignment of the variables which
violates none of the constraints.
AUTOASSIGN
uses
the following link and assignment variables. Associated with each spin system is an N-link variable, a
C-link variable, and an (amino acid) assignment variable. The domains of the two link variables associated
with a spin system initially include all of the other
spin systems. Aminoacids have only a (spin system)
assignment variable; the N- and C-links are simply the
two surrounding amino acids in the sequence. The domains of the assignment variables of spin systems and
amino acids are complementary. For example, each
Ala residue in the sequence is initially included in every ALAspin system’s domain of possible assignments,
and vice versa.
The goal of AUTOASSIGN
is to reduce each of these
domains to a single, unique value, or equivalently, to
assign a unique value to each of the assignment and
link variables. Traditionally, constraint satisfaction
problems have been solved by applying node-, arc-,
and path-consistency algorithms [Mackworth, 1977] to
prune the domains before any variable assignments
are made. Node- and arc-consistency algorithms can
be performed in polynonfial time, and in some cases
have been shown to reduce exponential search problems to linear execution times [Kumar, 1992]. These
algorithms assume however, that all of the constraints
are reliable and knowna priori. But in our case, constraints can only be inferred incrementally as analysis
progresses. Wedo not have space here to enumerate
all the ways in which constraints can be defined and
propagated, but a few examples are given to indicate
how these emerge.
The domains of a spin system’s link variables can
be constrained as follows. A first condition is that in
order for one spin system to be followed by another,
there must be a "reasonable" match between the first
spin system’s side-chain resonance frequencies and the
CO-ladder associated with the amide resonances of the
second spin system. Whenthis condition is not satisfied, the two spin systems can be removed from each
others’ C- and N-link domains respectively. A second
condition requires that all possible remaining link values be consistent with the order in which residue-types
occur in the sequence, as well as with the currently established sequence-specific assignments. For example,
if the CO-TOCSYdata suggests that some ALA-type
spin system is followed by some LEU-typespin system,
450
ISMB-93
but there is no instance of Ala-Leu in the sequence,
then the respective link domains should be pruned of
this inconsistency. Alternatively, if there is an instance
of Ala-Leu in the sequence but both of these residues
have already been assigned to other spin systems, then
the link domains of all unassigned ALAand LEUspin
systems can be pruned. Similar pruning is possible
when a spin system has been assigned to a particular
anfino acid but one or both of its link variables remains
unassigned.
The domains of the assignment variables can also
be constrained according to the links which have been
established. For example, once two or more spin systems have becomelinked to form a sequential segment,
the domains of their amino acid assignment variables
should be pruned for mutual consistency. The spin
system assignment domains of amino acids can also
be pruned as possible links between spin systems are
eliminated. Specifically, if a spin system currently included in an amino acid’s domain of possible assignments no longer has any way of establishing either an
N-link or a C-link which can support this hypothesis,
then AUTOASSIGN
removes that spin system from
the residue’s domain.
All of these methods for domain-pruning correspond
in principle to arc- and path-consistency arguments.
In effect, each of these is a mechanismfor "ruling-out"
inconsistent assignments. But very little information
of this type is available initially, and it is only by alternating between ruling-out and ruling-in mechanisms
that the system can progress to a complete assignment.
In particular, this incremental approach allows the system to base its earliest decisions on only the strongest
empirical evidence, and to subsequently use these most
reliable inferences to filter out manyof the errors that
might otherwise occur. Some of the mechanisms by
which assignments are ruled-in are discussed in the
following section which describes how these embedded
variables are represented.
Representation
and Implementation
Table 1 summarizesthe data structures used to represent the relationships between spin systems, sequencespecific amino acids, and CO-ladders. Each spin system is represented by an object whose attributes specify the spin system’s internal resonance frequencies, the
three embedded variables described in the preceding
section, plus three additional slots used to track the
domains of these variables. Tracking the domains of
the link variables is a bit more complicated than implied by our previous discussion. Each spin system
for which a CO-ladder could be identified maintains a
pointer to that ladder (under the attribute CO-ladder).
The domain of that spin system’s N-link variable is
then defined as the other spin systems whose side-chain
resonances matched those in the CO-ladder. These
matches are stored with the CO-ladder however, so
are accessed indirectly. Similarly, the domain of the
C-link variable is defined to be those other spin systems whose CO-ladders matched the side-chain values
of the spin system under consideration.
These COladders are listed in the Matches slot. Access to the
actual domainvalues is again indirect, as the spin systems associated with these ladders are stored with the
ladders themselves.
Bach amino acid in the sequence is also represented
by an object whose attributes include the N- and Clinks, the spin system assignment variable, and its associated domain. The attributes of a CO-ladder specify
the spin system associated with that ladder in the XZplane, the CO-TOCSY
peaks included in the ladder, a
list of other spin systems whose side-chain resonances
match the ladder, and a heuristic score reflecting how
reliable the ladder is. This score is a linear function
of the number of peaks included which occur on other
ladders, the number of overlapping ladders, and the
scatter of x and z values in the included peaks.
Defining what constitutes a "good" match between a
spin system’s y-values and the peaks (rungs) included
in a ladder is complicated by noise, degeneracy, and
incompleteness. Wehave found it useful to apply a
"measure of goodness" to matches as well as to COladders. The link-score between two spin systems is
then taken as the product of these two scores. Match
scores are computed as:
P9 x pr x (#matches
~ol /
P9 and pr represent the percentage of matched y-values
for the spin sytem and the percentage of matched rungs
for the ladder. The third term represents the total
number of matches occurring between the two objects,
less the sum of errors (err) which occurred in matching,
normalized by the match tolerance (to/) used.
Ruling in Variable
Assignments
In this section we describe several mechanismsfor reliably ruling in certain variable assignments. In order
to set a "high-link", a spin system’s best match to
a CO-ladder must also be that ladder’s best match
to any spin system, and the link-score between the
two spin systems must surpass all other link-scores
by a significant threshold. A second way of setting
links roughly corresponds to what has been referred
to as k-consistency algorithms [Cooper, 1989]. Using
a branching factor B, all possible paths from the Nand C-termini of all previously assigned segments are
generated. Whentwo such paths moving in opposite
directions cross each other and the only way to reach
certain unlinked spin systems is via these paths, the
implied "mutually-exclusive" links are committed to
for these spin systems. Because some of our implied
constraints maybe unreliable, we cannot use this principle in general to prune the domains. But when a
domain is forced by this mechanism to converge to a
single value, we have found that it is always the correct
one.
Figure 5: The Constraint Propagation Network.
Similar to the manner in which possible paths can
be used to impose "sequence-consistency" on the unassigned links of spin systems, it is possible to impose "match-consistency" on unassigned amino acids.
Working from the sequence, unique triples whose central residues have not yet been assigned can be identified. Then, if a single spin system has the requisite
links or matches consistent with this position, and very
high link-scores in both directions, the assignment to
the central amino acid is made. A second way of using unique triples is to allow the domains of the surrounding amino acids to constrain the spin system of
assignment of the central residue. Onceall such assignments have been evaluated, additional assignments can
be made by a process of elimination.
The Constraint
Propagation
Network
(CPN)
With each assignment of a variable, the entailed constralnts are immediately propagated to all other variables to ensure that global consistency is maintained
and that maximal pruning occurs with each decision.
There are two modules which are used to rule in variable assignments: make-assignment and establish-link.
Both of these are an integral part of the constraint
propagation network (Figure 5). Each of the ~rnlein modules" in turn triggers the "rule- out" modules
which remove possible links (matches between spin systems and CO-ladders) and possible assignments as described. In addition, the pruning of matches offers the
opportunity to re-examine peaks which may have been
inappropriately included on overlapped CO-ladders. If
a CO-ladder currently includes some peaks which no
longer have matches to any spin system’s side-chain
values, these peaks (rungs) can now be eliminated.
This has the effect of promoting both match scores and
ladder scores, thus allowing new constraints to emerge.
Control
Flow
Figure 6 gives an abstract representation of the overall
control flow and interaction
of AUTOASSIGN’s
four
Zimmerman
451
Object-Type
Spin-system
Attributes
X
Y-values
Z
N-link
C-link
AA-assigned
AA-domain
CO-ladder
Matches
N-link
Anfino Acid
C-link
SS-domain
SS-assigned
CO-ladder
Spin-system
CO-peaks
Matches
Lscore
Description
The H’~- frequency of this spin system
The side-chain proton frequencies of this spin system
The backbone XSNfrequency of this spin system
A spin system assigned to be this spin system’s predecessor in the sequence
A spin system assigned to be this spin system’s successor in the sequence
A sequence-specific amino acid assigned to this spin system
A list of possible anfino acid assignments for this spin system
A CO-ladder uniquely associated with this spin system’s x and z values
A list of CO-ladders whose rungs matched this spin system’s y-values
The preceding amino acid in the sequence
The following amino acid in the sequence
A list of possible spin system assignments for this amino acid
A spin system a~si~ned to this amino acid
A spin system uniquely associated with this ladder’s x,z-values
The CO-peaks which define this ladder’s rungs
A list of spin systems whose y-values matched this ladder’s peaks
A measure of intra~ladder scatter (noise) and inter-ladder separation (overlap)
Table 1: Objects Used in the Representation
main modules with the CPN. The initialization
routines create the objects described in Table 1 and initiaiize the domains of their embedded variables. The
first step in STARTUP,
which is invoked inm~ediately
after initialization, is to filter the domainsof the assignment variables based on spin system types and the
observed resonances of the spin systems. This step
narrows the possible assignments of certain AMX-and
LNG-typespin systems according to characteristic patterns that sometimes occur, and corresponds to nodeconsistency. The next goal is to assign the link attributes of as many spin systems as possible based on
the highest link-scores. The net effect of processing
inside STARTUP
is that the nmst reliable links and
assignments are established, while the number of remaining possible assignments and links is dramatically
rcduced (see results in Table 2).
CYCLEalternates
between establishing
definite
links by discovering convergent paths and making deftnite assignments by analyzing unique triples. Paths are
generated with a fixed branching factor until no further
links can be established. At that point, unique triples
are analyzed, and if any assignments are made, the algorithm returns to trying to establish links. Whenno
further progress can be made the module WlZAPUP
is
executed. At this point, all but the most degenerate
ladders have been pulled apart by gradually removing
the unmatched rungs as possible links (matches) are
eliminated. The most problematic cases occur when
a spin system motif is repeated two or more times in
the sequence, or when spin systems have severely overlapped backbone resonance frequencies. In order to
pull these ladders apart, the peals included in each
ladder are now redefined using a much smaller radius
centered about the spin system’s x and z values. We
also tested the use of these tighter match criteria in
452
ISMB-93
CPN
Initial
. ~
applic~on
II
Iterative I
IFinal
co mt I /
| processing
l~ocess’mgj
Figure 6: The Overall Control Flow of Execution
the x and z dimensions during the initialization
of
CO-ladders, but found that many of the true crosspeaks were then excluded from their appropriate ladders. WRAPUP
also uses the current assignments of
amino acids to constrain those that remain unassigned.
Backtracking
Situations arise where a request is sent to the CPNto
establish an assignment which conflicts with the current matches and/or established links. For example,
if links have been established between two spin systems and one of these is subsequently given a sequencespecific assignment, then the next round of constraint
processing will try to assign the other spin system to
the adjacent position in the sequence. But before nmking requested assignments, the CPNchecks to see if any
contradictions will result - e.g., a newly assigned spin
system becomes adjacent to some previously assigned
spin system with which it has no way of establishing
a link. Whena contradiction is discovered, the assignment is not made. Instead, the system evaluates the
competing assignments and links and attempts to determine where the error has occurred. In most cases,
the correct decision can be made based on the simple
scoring mechanisms used to evaluate matches, links,
and ladders. Once the error has been identified, the
offending link or assignment is retracted along with
any other actions which may have propagated from it,
and AUTOASSIGN
resumes execution.
Although not shown in Table 1, each of the objects also keeps track of a few local "history" variables
to facilitate backtracking. Aminoacids and spin systems maintain a list of possible assignments which have
been eliminated. Similarly, CO-ladders and spin systems maintain a list of matches which have been ruledout. Whenit becomes necessary to restore a previous
state, these lists are scanned, and any values which do
not conflict with currently assigned variables are restored. This actually works fairly well, but provides no
way of ensuring that only all of the constraints which
may have been propagated erroneously are retracted.
An important issue is whether or not the additional
storage and complexity of more detailed bookkeeping
would be worth the trade-off in performance. The current mechanisms form a preliminary foundation for future development of efficient backtracking schemes.
Performance Results
Table 2 shows the results obtaind for a 72 amino acid
domain derived from the Staphylococcal Protein A using the actual data obtained from a 3D CO-TOCSY
triple resonance experiment [Lyons e~ al., 1993b] and
a simulated data set for the same protein molecule.
The four columns show respectively the number of remaining possible assignments, the number of confirmed
assignments, the number of remaining possible links,
and the number of these which have been established.
Each row correpsonds to one of the stages of execution,
i.e.,
INIT, STAlZTUP, CYCLEand WRAPUP.For the
simulated data (results shown in parentheses), all
the expected crosspeaks were computed from the spin
system list and then analyzed with match tolerances
of +0.02 ppm, 4-0.08 ppm, and 4-0.35 ppmin the x, y,
and z dimensions respectively. This domain of Protein
A is composedof three helices and a 15 residue leader
sequence which has a random coil conformation, and
manyof its backbone amide frequencies are very similar. Accordingly, the degeneracy of x and z values is
fairly pronounced, and the initial CO-ladders are overlapped with one another. This problem is overcome
by the system as well-separated regions are assigned
first, and the subsequent elimination of inconsistent
matches permits substantial pruning of the degenerate
ladders. For these simulated data, the system makes
over 83% of the assignments in STARTUP
before resorting to iterative constraint processing. One pass
through CYCLEcompletes the assignments without
any errors (Table 2).
Having demonstrated the reliability
of the system
AA
Dommn
1378 (1378)
53e
105
2
Link
Assigned Dommn
o (o) ebe (sea)
(28) 22(so) 294 (85)
(0) 55(72) 103 (71)
(o) 7o(72) 66 (71)
Linked
o (o)
18 (81)
40 (71)
6e (71)
Table 2: Results on Real and (Simulated)
Protein A
Data for
using simulated data, we next carried out automated
analysis of the real 3D CO-TOCSYdata. Compared
to the simulated data, the real data contains only 65%
of the expected crosspeaks. The spin system list is
also incomplete as only 71 spin systems were identified for 72 residues in the sequence. The initial x, y,
and z match tolerances estimated from clustering of
the crosspeak frequencies were the same as those used
in the analysis of simulated data. With these real data,
early constraint processing (STARTUP)yields a dramatic reduction in the number of possible assignments
and matches, but only about 30%of the definite assignments. Iterative constraint processing inside CYCLE
results in assignments for all but 16 of the 71 spin
systems. Two instances of backtracking occur, and
in both cases consistent assignments are found once
the inconsistent assignments have been retracted. The
final stage of processing (WRAPUP)
yields an additionai 15 assignments. The remaining two residues in
the sequence, Met(-14) and Gln(-5), are both LNGs,
but neither is assigned to the single remaining LNG
spin system, as there is nothing in the CO-TOCSY
data to support a decision either way.
In evaluating the system’s performance, we observed
that no matches were incorrectly eliminated, but in one
case, His(-4), the correct assignment has been deleted
from the appropriate spin system’s donmin of possible
assignments. This is due to the fact that the expected
crosspeaks to both the preceding and succeeding spin
systems in the sequence were not detected in the NMR
experiment. However, in the final stages of WRAPUP,
the correct assignment is made by a process of elimination, as there is only one remaining AMX-typespin
system and His(-4) is the only remaining unassigned
AMX-typeresidue.
Related
Work
Automated Sequential
Assignment
Because through-space interactions often occur between the protons on adjacent residues, nuclear Overhauser effect (NOE) data used to measure throughspace distances has also been used routinely in
manual analysis to infer connectivity information
[Wuethrich, 1986]. Attempts to automate sequential
assignment using 2-D NOEdata have had limited success, largely because the solution is greatly underconstrained by the connectivity information. The
problem with inferring spin system adjacencies from
Zimmerman453
NOEdatais twofold:
(I)through-space
interactions
alsooccurbetween
no~-adjacent
residues,
and(2)the
occurrence
of "through-space
adjacent"
interactions
is
conformation
dependent.
In onecase[Billeter
et aL,1988],the systemwas
testedon both real and simulateddata sets and
couldtypicallymake only 30-50%of the complete
assignments. Similar results were achieved in a
semi-automated implementation reported by Ends and
Kuntz (1989). The system first establishes the most
reliable links on the basis of strong supporting evidence in the data, and then writes a list of potential
"next" and "previous" spin system relations to a separate file. This information is then used by the expert
to make manual assignments. Using bovine pancreatic trypsin inhibitor (BPTI) as a test case, manual
analysis of the established links led to 21 unambiguous assignments (41% of the sequence), and logical
consistency arguments similar to those used by AUTOASSIGN
were then applied to make an additional
23 assignments by a process of elimination. It is interesting to note that the percentage of assignments
which can be most reliably established by AUTOASSIGNfor Protein A fall within the range reported by
Billeter et al (i.e. 30%in STARTUP),
and that the percentage of additional assignments obtained by extensive constraint propagation qualitatively agrees with
the results of leads and Kuntz, 1989]. Although several authors (Montelione and Wagner, 1990; Ikura e$
al, 1990; Logan et al, 1992; Montelione et al, 1992;
Lyons and Montelione, 1993a; Lyons et al, 1993b) have
noted that the new data sets being generated by various multiple-resonance
multi-dimensional NMRexperiments (such as the CA-TOCSYand CO-TOCSY
experiments) are more amenable to automated analysis, no fully automated systems have yet been reported. A recently published semi-automated implementation called ALFA[Bernstein et al., 1993] uses
energy minimization techniques to make sequential assignments. The connectivity information is taken from
three-dimensional
NOESYdata. In ALFA, all spin
systems are initiMly given unique but arbitrary assignments to amino acids in the sequence. The system
then proceeds to examine arbitrarily selected pairs of
segments of random lengths varying from two to seven
residues. The current assignments of these residues
are exchanged wherever such a modification will lead
to a reduction in the total "energy". Terms in the energy equation include a measure of spin system-residue
type compatibility and detected sequential crosspeaks
to surrounding spin systenm. This process is repeated
until no further minimization is possible. For the single test case reported, the system made 83%correct
assignments using the NOEdata.
Dynamic Constraint
Satisfaction
In most constraint satisfaction problems, the variables,
domains, and constraints are included in the problem
454 ISMB--93
specification, and the solution space can be dramatically reduced before search is initiated by applying various consistency algorithms. In AUTOASSIGN,
only
the variables, their domains, and unary constraints are
available initially. In our "constraint graph", we have
all of the nodes (variables) but none of the edges (binary or n-ary constraints). Instead, these emergeas dependency relations amongamino acids, spin systems,
and CO-ladders as the links and assignments are established. A second advantage in knowingall the constraints a pr/or/is that the order in which decisions are
made can be guided by "least-commitment" or "mostconstrained-first" strategies. One possibility would be
to do a preliminary dependency analysis which might
be able to anticipate the more important choice points,
e.g., which links or assignments will trigger the maximumnumber of additional assignments.
Synthesis tasks (e.g. configuration, design, etc.)
have also been characterized as dynamic constraint
satisfaction problems [Mittal and Falkenhainer, 1990].
But in these tasks, not even the variables themselves
are predetermined. Thus the focus is often on establishing a meansof coupling the creation of variables to
the propagation of the constraints they entail. In our
own experience with the ACONS
configuration system
[ttagerty e~ al., 1991], we addressed this issue by distributing the constraint information over the objects
being constrained rather than storing it in a central
location such as a goal stack. Although the creation of
variables is not an issue for AUTOASSIGN,
we have
found the distributed representation of object-specific
state information to be an effective means of reducing
search. A second principle applied in both ACONS
and
AUTOASSIGN
is the thorough propagation of constraints as eachcommitment
is made.
Conclusions
AUTOASSIGN
demonstrates that generic constraintsatisfaction methods can be successfully adapted to a
complex real-world problem. The use of these methods evolved naturally in the course of trying to model
the type of reasoning the expert brings to bear on the
sequential assignment problem. It is difficult to compare the performance results of systems which perform
the same task using different inputs, particularly when
each system has only one real data set to work with.
Further testing and development on additional proreins is needed to better assess the system’s strengths
and weaknesses and to enhance its robustness and flexibility.
Qualitatively however, AUTOASSIGN
appears
to outperform other systems designed to perform the
same task which have been reported to date.
The sequential assignment problem is a special type
of dynamic constraint satisfaction problem, where the
variables and domains are given but the constraints
must be discovered in the process of analyzing the data.
This description fits manydata interpretation problems, and it would be interesting to explore howwell
the approach we have taken maps to other domains.
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